EAST YORK COLLEGIATE
INSTITUTE
MCV4U Course Outline 2012-2013
This Course Outline is based upon the Ministry of Education and Training Ontario Curriculum for Grade 12 Mathematics
as per the revised document of 2007.
Board: Toronto District School Board
School: East York Collegiate Institute
Curriculum Leader: R.Singh
Developing Teachers: H.Odintsova
Date of Revision: June 2012
Course Title: Calculus and Vectors, Grade 12, University Preparation
Grade: 12
Code: MCV4U
Credit Value: 1.0
Prerequisite: Advanced Functions, Grade 12, University Preparation (MHF4U)
Textbooks: Advanced Functions and Introductory Calculus, Harcourt (2002)
Geometry and Discrete Mathematics, Harcourt (2002)
Resources: Calculus and Vectors 12, McGraw-Hill Ryerson (2008)
Calculus and Vectors 12, Nelson (2008)
Algebra and Geometry, Holt, Rinehart and Winston (1988)
Teacher-made Worksheets
Graphing Calculators & Computers
Course Description
This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students
will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in threedimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential,
rational, and radical functions; and apply these concepts and skills to the modeling of real-world relationships. Throughout the course,
students will engage in the following processes: Problem Solving, Reasoning and Proving, Reflecting, Selecting Tools and
Computational Strategies, Connecting, Representing and Communicating. This course is intended for students who choose careers in
fields such as science, engineering, economics, and some areas of business, including those who will be required to take a universitylevel calculus, linear algebra or physics course.
Strands
Rate of Change
Derivatives and Their Applications
Geometry and Algebra of Vectors
29 periods
25 periods
34 periods
Program Planning Considerations
Exceptional Students:
Additional time will be allowed for tests. Additional accommodations will be provided in
consultation with the Guidance, Special Education and ESL departments.
Technology:
Graphing Calculators, and Computers will be utilized for technology-related applications.
Career Education:
Links to related fields will be established throughout the course.
Co-operative Education:
These will be provided in association with Guidance Department.
Mathematics Anxiety:
Attention will be addressed according to the following:
• Cultural perspectives
• Positive reinforcements
• Variety of assessment techniques
• Group structures
• Consideration for Learning Styles
Learning Skills
Assessment of the learning skills will be done on an ongoing basis throughout the academic year by observations of students at work,
checklists and interviews. This will include:
Classwork/homework
(Work habits, homework and organization)
Completed work and seeking assistance (Organization and initiative)
Persistence and independence at tasks (Working independently and initiative)
Extension of task
(Organization and initiative)
Achievement of group goals
(Team work)
Assessment Strategies
A variety of teaching/assessment strategies to address students’ needs will be used during the school year. Formative assessments will
be ongoing through out the academic year. These may include:
• Diagnostic assessment
• Formative assessment
• Performance assessment
• Portfolio assessment
• Rubrics
• Checklists
Term Summative Evaluations (70% Term Work)
• Tests, quizzes, tasks and other forms of term summative evaluations will occur throughout the academic year at the end of
units of work as outlined in the accompanying course outline.
• Students will be provided with reasonable opportunities to master skills relating to the achievement of the curriculum
expectations before assessment and evaluation occurs.
• Major evaluations will be announced at least one week in advance.
• Accommodations will be made for school activities, statutory holidays, religious days, cultural days, sports events and other
occurrences that may impact on any scheduled evaluation. It is the student’s responsibility to notify teachers of such absences
in advance and to make up missed work.
• Absence on the day of an evaluation must be documented. If a student must miss an evaluation, s/he is expected to:
a) see the teacher before the absence to arrange for an alternative date to make up the evaluation; or
b) in case of illness or unexpected absence, present a note to the teacher, signed by a parent or guardian, immediately
upon their return to explain the absence. An alternate evaluation will then be scheduled at a mutually convenient time.
• The East York Late Policy applies to all assignments and evaluations. See your Agenda book.
• Cheating will not be tolerated in any form and will be dealt with appropriately.
Final Mark Calculation
Calculation of the Term Mark will be based upon the Categories of the Achievement Chart. This chart is meant to assist teachers in
planning instruction and learning activities for the achievement of the curriculum expectations. It is also used in designing assessment
and evaluation tools and in providing feedback to students. Each mathematical topic will contain each category in the chart due to the
integrated nature of the discipline in mathematics. Final marks will be calculated as follows:
Term Work:
Knowledge and Understanding:
Application:
Thinking and Inquiry:
Communication:
Final Summative Evaluation
Reporting
Report #1
100% Term Work
70%
Levels of Achievement:
Level 1: 50 - 59%
Level 2: 60 – 69%
Level 3: 70 – 79%
Level 4: 80 - 100%
35%
35%
15%
15%
30%
Report #2
100% Term Work
(Cumulative)
70% Term Work +
June Report
30% Final Summative Evaluation
(Cumulative)
Communication
Access to extra help and mark records. Students are encouraged to consult their teachers on a regular basis for extra help and
guidance as it relates to improving their academic performance. Students are also expected to discuss strategies for improving their
grades with their teachers. Students are expected to view their report cards as an indication of their current achievement and discuss
with teachers for clarification.
Communication with Parents/Guardians. Comments pertaining to academic achievement and learning skills are placed on the report
cards are primarily to provide feedback for parents/guardians as well as students. Parent/guardian nights can be used for one to one
discussion. At times it may be necessary to contact parents/guardians by telephone to discuss a student’s performance.
Parents/guardians are also encouraged to contact teachers as and when the need arises.
EAST YORK COLLEGIATE
INSTITUTE
MCV4U Daily Course Outline 2012-2013
Textbooks: Calculus and Vectors (Nelson)
Strand #1: RATE OF CHANGE (29 periods)
Overall Expectations:
•
To demonstrate an understanding of the rate of change by making connections between average rate of change over an interval and
instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of limits;
•
To graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and
algebraic representations of a function and its derivative;
•
To verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial,
sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related functions.
Per #
UNIT #1:
1&2
3
4, 5, 6
7
8
9 & 10
11
12
13
TOPIC
INTRODUCTION TO CALCULUS (13 periods)
Evaluating Limits Graphically
Piecewise-defined Functions
Evaluating Limits Algebraically
Continuity
TEST #1
The Slope of a Tangent Line
The Derivative Function using First Principles
Review
TEST #2
UNIT #2: DERIVATIVES (9 periods)
1&2
Derivatives of Polynomial Functions
3&4
Derivative of a Product of Functions
5
Derivative of Rational Functions
6&7
Derivative of Composite Functions
8
Review
9
TEST #3
Section
AFIC
3.3
3.3
3.4
3.5
3.1
4.1
4.2
4.3
4.4
4.6
ASSIGNMENT
Supplementary Resources
p 97-99, # 4–10, 12, 13
p. 99, #11
p 105-107, # 1–19
p 110-112, # 1–14
Limits sheets
Lesson sheet
Practice sheet
p 83-86, # 6, 11, 18 – 20
p 130-132, # 1, 5, 6, 9, 10, 12
p. 115 #1-3, 7-12, 17, 18
p 138-140, # 1–26
p 145-146, #1–8,10–12
p 149-150, # 1–12
p 158-160, # 1–15
p. 163, #1-20
UNIT #3: DERIVATIVES OF EXPONENTIAL & SINUSOIDAL FUNCTIONS (7 periods)
1
The Derivative of y = ex
8.1
p 302-304, # 1–14
2
The Derivative of y = lnx
8.2
p 309-311, # 3-11
Derivatives of General Exponential
8.3
p 315-317, # 1–9
3
& Logarithmic Functions
4
Derivatives of y=sinx, y=cos x & y=tanx
Appendix p. 400, #1, 2, 5
A2
5
More Derivatives of Trigonometric Functions
6
Review
p. 330, #1-17 (select)
7
TEST #4
Review sheet
De-emphasize Quotient Rule
Review sheet
Practice sheets
Review sheets
Strand #2: DERIVATIVES AND THEIR APPLICATIONS (25 periods)
Overall Expectations:
•
To make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the
connections in curve sketching;
•
To solve problems, including optimization problems, that require the use of concepts and procedures associated with the derivative,
including problems arising from real-world applications and the development of mathematical models.
Per #
TOPIC
UNIT #4: CURVE SKETCHING (10 periods)
1
Increasing and Decreasing Functions
2
Critical Points and Relative Maxima/Minima
3
Asymptotes
4
Concavity and Points of Inflection
5&6
An Algorithm for Graph Sketching
7&8
Exponential & Logarithmic Functions
9
Review
10
TEST #5
Section
AFIC
9.1
9.2
9.3
9.4
9.5
ASSIGNMENT
Supplementary Resources
p 342-344, # 1–11
p 349-351, # 1–13
p 361-362, # 1–14,
p 369-371, # 1-13
p 375, # 1–8
See Summary Sheet
& Assignment Sheets:
Can introduce all topics at the
beginning and make graphs
more complicated over 6
periods.
p. 378, #2-12
Review Sheet
Per #
TOPIC
Section
UNIT #5: APPLICATIONS OF DERIVATIVES (15 periods)
1&2
Higher-Order Derivatives;
5.2
Velocity & Acceleration,- Straight Line Motion
3&4
Rates of Change
3.2
5&6
TEST #6
Maximum/Minimum on an Interval
5.4
7, 8 & 9 Optimization Problems
5.5
10 & 11 Optimizing in Economics & Science
5.6
12
Optimization Problems – Exponential Functions
8.4
13 & 14 Review
15
ASSIGNMENT
Supplementary Resources
p 185-188, # 1–15, (#16–19)
Blob Demo with TI-83
Lesson & Exercise sheets
Problem Sheet
p 92-94, # 1–19
p 200-202, # 1–12
p 206-208, # 1–18
p 213-216, # 1–12
p 320-323, # 1–14
p. 219-222, #10, 13-16, 24-31
p. 331, #11-15
Assignment Sheets
Assignment Sheets
Assignment Sheets
Review Sheets
TEST #7
Strand #3: GEOMETRY AND ALGEBRA OF VECTORS (34 periods)
Overall Expectations:
•
To demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by
recognizing their applications;
•
To perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including
those arising from real-world applications;
•
To distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and threespace, and determine different geometric configurations of lines and planes in three-space.
UNIT #6: VECTORS (6 periods)
1
Vector Concepts
2
Vector Laws
3
Force as a Vector
4
Velocity as a Vector
5
Review Exercise
6
MGA
4.1
4.2
4.3
4.4
Review Sheet
p 166 #1, 2, 3, 6, 7, 13, 19
p. 166, #4, 5, 8-12, 14, 17, 22
p 172 #2-4, 6-9, 12, 13, 17, 18
p 178 #1-19 (select)
p. 192 #1, 3, 5, 9-11, 13, 15, 17
p 185 #197, 9, 10
p 192 #6-8, 18
p 194 #1-17
p 197 #1-7
Review Sheet
TEST #9
UNIT #8: LINES IN A PLANE (8 periods)
1
Parametric and Vector Equations of a Line
2
The Scalar Equation of a Line in a Plane
3
Equations of a Line in 3-Space
4
Distance Formulae in 2- & 3-Space
5&6
7
The Intersection of Two Lines
Review Exercise
8
TEST #10
UNIT #9: EQUATIONS OF PLANES (10 periods)
1
The Vector Equation of a Plane in Space
2&3
The Scalar Equation of a Plane in Space
4
The Intersection of a Line and a Plane
5
Sketching Planes
6
The Intersection of Two Planes
7
Using Matrices
8
The Intersection of Three Planes
9
Review Exercise
10
#2, 6-12
#1, 3, 4, 6, 7, 11, 18, 20
#6, 7, 12, 13, 18, 19, 22
#2, 3, 4, 5, 8, 10, 11
#1-19
#1-8
TEST #8
UNIT #7: ALGEBRAIC VECTORS & APPLICATIONS (10 periods)
1
Algebraic Vectors in 2-Space
5.1
2
Algebraic Vectors in 3-Space
5.1
3
Operations With Algebraic Vectors
5.2
4
The Dot Product of Two Vectors
5.3
5
Applications of the Dot Product
5.5
6
The Cross Product of Two Vectors
5.4
7
Applications of the Cross Product
5.5
8&9
Review Exercise
10
p 127
p 133
p 142
p 149
p 153
p 155
7.1
7.2
7.3
7.2
7.3
7.4
p 245
p 251
p 256
p. 252,
p. 258,
p 263
p 266
p 270
#1-16 (select)
#1-9
#1-12, 14 (select)
#11, 12
#15
#1-11
#1-15
#1-7
8.1
8.2
8.3
8.3
8.4
8.4
8.5
p 279
p 285
p 292
p. 293,
p 300
p. 301,
p 308
p 312
p 315
#1-10
#1-13
#1-3, 7, 8
#4-6, 9-11
#1-3
#6, 8, 9
#8
#1-22
#1-7
TEST #11
Cumulative Review (Units #1-9)
FINAL SUMMATIVE EVALUATION (30%)
Lesson & Assignment Sheet